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What is RTI for mathematics?

Page 5: Progress Monitoring

Progress monitoring is a form of assessment in which student learning is evaluated on a regular basis (e.g., weekly, every two weeks) to provide useful feedback about performance to both students and teachers. The primary purpose of progress monitoring in RTI is to determine which students are not responding adequately to instruction. Progress monitoring also allows teachers to track students’ academic progress or growth across the entire school year. It is used in the following ways at the different levels of instruction:

Tier 1 — Students identified through the universal screening are monitored to assess their response to high-quality core instruction.

Tier 2 — Students are monitored to assess their response to Tier 2 intervention.

Tier 3 — Students are monitored to assess their response to intensive intervention; additionally, teachers can use progress monitoring data to tailor their instruction to meet the individual students’ needs.

One common type of progress monitoring is curriculum based measurement (CBM), sometimes referred to as general outcome measurement (GOM). These assessments are useful because:

Tests (sometimes referred to as probes or measures) take only a few minutes to administer and score and may be given to groups of students.

Each probe includes sample items from every skill taught across the academic year.

Probes, administration, and scoring are standardized to produce reliable and valid results.

Scores reflect even the smallest changes in student improvement.

Research shows that CBM scores are highly correlated to those on standardized tests.

Graphs of each student’s scores offer a clear visual representation of her or his academic progress.

Brad Witzel discusses why it is important to use a curriculum based measure that assesses skills a student encounters across the year as opposed to a mastery measurement probe that assesses a single skill (time: 0:44).

For Your Information

Depending on the availability of resources, a teacher might choose to monitor the progress of all students in the general education classroom, and not just those who happen to be struggling. Doing so can indicate whether students are receiving high-quality instruction. Students receiving high-quality instruction will show increased mathematics performance levels and rates of growth across the year. If all students are not demonstrating sufficient improvement in their mathematics skills, inadequate instruction might be the reason, and progress monitoring data can be useful in helping the instructor to tailor instruction to meet the needs of the class.

As we mentioned previously, GOMs can be used to screen students, as well as to identify those who might struggle with mathematics. They can also be used to monitor the progress of students and determine which are not responding to instruction. In mathematics, teachers should administer two types of probes: computation probes and concepts and applications probes. Click on the links below to view samples of each. Note: Because GOMs can be used for universal screening, the examples below are the same as those shown on Page 3.

* No valid middle or high school concepts and applications probes are available at this time.

For Your Information

The National Center on Intensive Intervention provides a tools chart that presents information about commercially available progress monitoring probes that have been reviewed by a panel of experts and rated on key features.Click here to use this tool chart.

There is a lack of available validated measures to assess the mathematics skills of high school students. This is especially true of measures that assess students’ conceptual understanding. David Allsopp discusses an option for assessing this type of understanding (time: 1:56).

David Allsopp, PhDAssistant Dean for Education and PartnershipsUniversity of South Florida

Keep in Mind

To track student growth across time, each probe includes sample items from skills taught throughout the academic year. Though students are at first expected to correctly solve relatively few problems, their scores should improve as the academic year progresses and they learn new skills and concepts.

Lynn Fuchs talks more about the benefits of using progress monitoring probes that sample the entire year’s curriculum (time: 1:57).

Lynn Fuchs, PhDDunn Family Chair in Psycheducational AssessmentDepartment of Special EducationVanderbilt University

Administering, Scoring, and Graphing Progress Monitoring Probes

Every progress monitoring probe has specific administration and scoring guidelines that instructors should carefully follow to ensure fidelity and accuracy of measurement. Students’ scores should be graphed to create a visual representation of student performance over time.

Probes are timed, and students complete as many problems or questions as possible in the allotted period. To restate: Individual administration is required when early numeracy skills like oral counting or identifying numbers are being assessed. In the case of older students, group administration typically ranges from two to ten minutes, depending on the grade level and the type of measure. When feasible, teachers can administer computer-based screening measures.

Each time student progress is measured, an alternate form of the probe should be administered. Student progress is monitored using the same procedures and measures across all intervention levels; however, the frequency of progress monitoring may vary:

Tier 1 — In general, at least once a month; every week or every other week for students identified as struggling by the universal screening

Tier 2 — At least once per week

Tier 3 — Once or twice per week

Tips for Administering Probes

Educators should establish consistent administration procedures. Doing so will allow them to compare students’ performance across time to be sure their scores are accurate reflections of their ability and not the result of inconsistent administration.

Educators should administer both computation probes and concept and application probes at the same time of day, back to back, and in the same order.

For students with disabilities whose IEPs specify accommodations, educators should make sure those students receive the accommodation every time a probe is administered.

For Your Information

During core instruction, teachers might need to monitor the progress of students whose universal screening scores are slightly above the benchmark weekly or every other week. Although currently performing in the expected range, these students might be at-risk for experiencing difficulty with mathematics at a later date. Ongoing progress monitoring helps teacher detect these difficulties relatively quickly.

In general, scoring a computation or a concepts and applications probe is simply a matter of determining how many items the student solved correctly. Commercially available probes include detailed scoring procedures that are standardized to produce reliable and valid scores. Incorrect scoring can lead to inaccurate and misleading conclusions.

In the case of elementary students, computation probes can be scored either according to the number of digits correct or by the number of correctly answered problems. Regardless of which method they choose, teachers in all classes and grades at a given school should score probes in the same way so that the scores are comparable. Click on the links below for examples of scored probes.

Lynn Fuchs, PhDDunn Family Chair in Psycheducational AssessmentDepartment of Special EducationVanderbilt University

For students in middle and high school, scoring probes using digits correct is not recommended. Instead, problems should be scored by the number of problems correct. In the case of multi-step problems, partial credit can be given for correctly performed steps. Brad Witzel discusses the reasoning behind this latter approach (time: 1:04).

Most companies that provide progress monitoring measures also include a tool that scores and graphs student data. Alternatively, the teacher or the student can graph the data on paper or by using a graphing program or application. Regardless, by examining the data on the CBM graph, the teacher can determine whether a student is making adequate progress.

To the right is a sample CBM graph. The vertical axis (y) represents the range of possible scores a student can obtain on the progress-monitoring probe (e.g., the number of problems correct). The horizontal axis (x) represents the number of weeks of instruction. It is recommended that—for students receiving supplemental or intensive intervention—scores should continue to be plotted on their existing progress monitoring graphs. The instructor should draw a dotted vertical line to indicate when a new intervention begins (e.g., changing from supplemental or intensive intervention). This will allow school personnel to compare progress made during the different tiers of intervention.

For Your Information

Students who are aware of their progress are more knowledgeable about their learning. When they see their academic growth in an easily understood format-such as on a graph-students begin to recognize the relationship between their efforts and progress. The benefits of using graphs in this way include:

Offering students a visual representation of their progress

Providing students with evidence that their hard work is paying off

Motivating students to continue their efforts or to work harder

For more information about how to administer, score, and graph progress monitoring data, please visit the IRIS Module and Case Study Unit:

The IRIS Center Peabody College Vanderbilt University Nashville, TN 37203 iris@vanderbilt.edu. The IRIS Center is funded through a cooperative agreement with the U.S. Department of Education, Office of Special Education Programs (OSEP) Grant #H325E170001. The contents of this Website do not necessarily represent the policy of the U.S. Department of Education, and you should not assume endorsement by the Federal Government. Project Officer, Sarah Allen.